[Haskell-cafe] Tutorial: Curry-Howard Correspondence

Dan Weston westondan at imageworks.com
Thu Oct 18 17:46:03 EDT 2007

It was I that he quoted, and now I am totally flummoxed:

thm1 :: (a -> a) -> a
thm1 f = let x = f x in x

 > thm1 (const 1)

I *thought* that the theorem ((a => a) => a) is not derivable (after 
all, 0^(0^0) = 0^1 = 0), but it appears somehow that thm1 is a proof of 
its type.

Help, I just unlearned everything I ever thought I new about the C-H 

jerzy.karczmarczuk at info.unicaen.fr wrote:
> Tim Newsham quotes somebody /I didn't follow this thread!/:
>>> I assume you mean then that it is a valid proof because it halts for 
>>> *some* argument? Suppose I have:
>>> thm1 :: (a -> a) -> a
>>> thm1 f = let x = f x in x
>>> There is no f for which (thm1 f) halts (for the simple reason that 
>>> _|_ is the only value in every type), so thm1 is not a valid theorem.
> =================
> Since, as I said, I didn't follow you, it would be indecent of me to try to
> be clever now, but the statement above (that there is no f for which thm1
> halts) is false *IN HASKELL*. Try f = const 1.
> Unless I missed some important point elsewhere...
> Jerzy Karczmarczuk
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